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The REG Procedure |
Table 55.5 contains the summary statistics for assessing the fit of the model.
Table 55.5: Formulas and Definitions for Model Fit Summary StatisticsDefinition or Formula | |
n | the number of observations |
p | the number of parameters including the intercept |
i | 1 if there is an intercept, 0 otherwise |
the estimate of pure error variance from the SIGMA= option or from fitting the full model | |
SST_{0} | the uncorrected total sum of squares for the dependent variable |
SST_{1} | the total sum of squares corrected for the mean for the dependent variable |
SSE | the error sum of squares |
MSE | |
R^{2} | |
ADJRSQ | |
AIC | |
BIC | |
CP (C_{p}) | |
GMSEP | [( MSE(n+1)(n-2))/(n(n-p-1))] = [1/n] S_{p}(n+1)(n-2) |
JP (J_{p}) | [(n+p)/n] MSE |
PC | [(n+p)/(n-p)] (1 - R^{2}) = J_{p} ( [n/( SST_{i})] ) |
PRESS | the sum of squares of predr_{i} (see Table 55.6) |
RMSE | |
SBC | n ln( [ SSE/n] ) + p ln(n) |
SP (S_{p}) | [ MSE/(n-p-1)] |
Table 55.6 contains the diagnostic statistics and their formulas; these formulas and further information can be found in Chapter 3, "Introduction to Regression Procedures," and in the "Influence Diagnostics" section. Each statistic is computed for each observation.
Table 55.6: Formulas and Definitions for Diagnostic Statistics
Formula | |
PRED () | X_{i}b |
RES (r_{i}) | |
H (h_{i}) | x_{i}(X'X)^{-}x_{i}' |
STDP | |
STDI | |
STDR | |
LCL | STDP |
LCLM | STDI |
UCL | STDP |
UCLM | STDI |
STUDENT | [(r_{i})/( STDR_{i})] |
RSTUDENT | |
COOKD | [1/p] STUDENT^{2}([ STDP/( STDR^{2})]) |
COVRATIO | |
DFFITS | |
DFBETAS_{j} | |
PRESS(predr_{i}) | [(r_{i})/(1-h_{i})] |
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